Interplay of the CGC and TMD frameworks to all orders in kinematic twist

Abstract

A framework for an improved TMD (iTMD) factorization scheme at small $x$, involving off-shell perturbative subamplitudes, was recently developed as an interpolation between the TMD $k_t\ll Q$ regime and the BFKL $k_t\sim Q$ regime. In this article, we study the relation between CGC and iTMD amplitudes. We first show how the dipole-size expansion of CGC amplitudes resembles the twist expansion of a TMD amplitude. Then, by isolating kinematic twists, we prove that iTMD amplitudes are obtained with infinite kinematic twist accuracy by simply getting rid of all genuine twist contributions in a CGC amplitude. Finally we compare the amplitudes obtained via a proper kinematic twist expansion to those obtained via a more standard dilute expansion to show the relation between the iTMD framework and the dilute low $x$ framework.

42 pages, 7 figures, 1 table

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• The dipole form of the quark part of the BFKL kernel

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• One-Loop Corrections to Dihadron Production in DIS at Small $x$
• Single Inclusive Hadron Production in DIS at Small $x$: Next to Leading Order Corrections
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• The dipole picture and the non-relativistic expansion
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